Supporters of Teresa Sullivan, ousted president of the University of Virginia, claimed growing momentum to reinstate her on Monday, the eve of a meeting to resolve the school’s leadership crisis.

The 15 members of the Board of Visitors who are expected to vote Tuesday declined to share their views in advance of the meeting.

Most have indicated at least privately which way they expect to vote, according to some vote counters, but as many as four members remained uncommitted late Monday.

In recent days, Sullivan’s faction has secured support of influential groups, such as the deans of 10 U-Va. schools and the university’s Council of Foundations, a network of alumni and donors.

“We are optimistic,” said George Cohen, chairman of the Faculty Senate and a Sullivan backer. “I would imagine that the board would be very reluctant to have this meeting called unless there was going to be the decision that we are hopeful for.”

The university announced June 10 that Sullivan would leave after less than two years, throwing the Charlottesville campus into an uproar. She is scheduled to step down Aug. 15, with an interim president taking over the next day.

Sullivan, who had initially indicated to board members that she would return under certain conditions — including the resignation of her chief critic on the board, Rector Helen E. Dragas — on Monday signaled that she would agree to stay without a guarantee of concrete changes, according to three people familiar with the negotiations.

Dragas and her allies remain opposed to Sullivan’s return because they want faster changes in response to financial pressures. The battle has come to be seen as part of a larger debate about the mission of elite public universities.

“This is coming down to the Board of Visitors meeting on Tuesday,” said Walter Heinecke, an education professor who helped organize a rally Sunday. “These folks have the fate of the university in their hands.”

The board will meet at 3 p.m. in the Rotunda designed by Thomas Jefferson. The meeting will be open to the public, although it is likely the panel will enter a closed session at some point.

“Hopefully, it will be resolved,’’ said board member Vincent Mastracco, declining to comment further.

Dragas and other members did not return calls for comment. Sullivan and her attorney, Raymond Cotton, declined to comment.

Three board members — Charlottesville lawyer Hunter E. Craig, finance executive A. Macdonald Caputo and investment executive Timothy B. Robertson, son of televangelist Pat Robertson — asked for the meeting to reconsider Sullivan’s departure.

Others said to support Sullivan are medical executive W. Heywood Fralin, who voted against appointing an interim leader last week; former Democratic legislator Alan Diamonstein; and Mastracco, according to several people who have been tracking the vote count but declined to be named because of its sensitivity. Caputo, Fralin and Mastracco did not know about the plan to oust Sullivan until its final days, according to former board members and a university official with knowledge of the situation who was not authorized to speak publicly.

If those members continue to back her, that would give Sullivan at least six supporters.

At least five board members, according to the vote counters, are expected to oppose keeping her: Dragas; businesswoman Allison Cryor DiNardo; coal company founder Marvin Gilliam; beer distributor John Nau; and R.J. Kirk, a billionaire businessman from Radford.

That leaves, as potential swing votes, Dr. Stephen Long, investor Robert D. Hardie, lawyer George Martin and business lawyer Glynn Key.

Hardie and Caputo abstained last week when the board voted 12 to 1 to appoint commerce school dean Carl P. Zeithaml as interim president. Key was absent.

“We’re all waiting to see what happens,’’ former board member Syd Dorsey said. “I’m hopeful this will come to a quick resolution.”

Gov. Robert F. McDonnell (R) told board members Friday that if they do not resolve the crisis Tuesday, he will remove all of them. McDonnell plans no further announcements until after the vote, but his aides are fielding calls from those who want to share their opinions.

The board drew criticism for failing to take a vote on the removal of Sullivan. Instead, Dragas and Vice Rector Mark Kington told her they had 15 votes to remove her. She tendered her resignation.

If the board had taken a vote to remove her, it would have required a two-thirds majority, or 12 of what were 16 voting members. But Sullivan’s forced resignation was negotiated without a formal vote. It would take a simple majority of the board to reinstate her. That means eight of 15 members, because Kington resigned last week.

Also Monday, the Southern Association of Colleges and Schools, which accredits U-Va., questioned whether the school was in compliance with its standards relating to integrity and the faculty’s role in governance.

Staff writer Jenna Johnson in Charlottesville contributed to this report.